Firstly: 

Zakaat al-fitr must be paid before the Eid prayer, because of the report narrated by Abu Dawood (1609) and Ibn Majaah (1827) from Ibn ‘Abbaas (may Allaah be pleased with him) who said: The Messenger of Allaah (peace and blessings of Allaah be upon him) enjoined zakaat al-fitr as a purification for the fasting person from idle and obscene talk, and to feed the poor. Whoever pays it before the (Eid) prayer, it is accepted zakaah, and whoever pays it after the prayer, it is (ordinary) charity.

Classed as hasan by al-Albaani in Saheeh Abi Dawood. 

It says in ‘Awn al-Ma’bood Sharh Abi Dawood: It seems that the one who pays zakaat al-fitr after the Eid prayer is like one who did not pay it, because they both failed to pay this obligatory charity. Most of the scholars are of the view that paying it before the Eid prayer is only mustahabb, and they stated that it may be paid until the end of the day of al-Fitr, but the hadeeth refutes that. 

As for delaying it until after the day of Eid, Ibn Raslaan said: That is haraam according to scholarly consensus, because it is zakaah, so there must be sin involved in delaying it, as is the case with delaying prayer until the time for it is over. End quote. 

Based on this, the imam was wrong to delay the zakaah, and he should have looked for people who are entitled to it, or sent the zakaah to a country where there are people who are entitled to it. 

Secondly: 

If a person delays giving zakaat al-fitr until after the day of Eid for no valid reason, he has sinned and he has to make it up. The people of the mosque are not to blame, because they appointed someone to give it on their behalf. The imam now has to give it to people who are entitled to it. It is not permissible to spend it on mosque expenses. As for the Islamic school, if there are poor people there who are entitled to the zakaah, it is permissible to give it to them, otherwise it is not. 

Ibn Qudaamah (may Allaah have mercy on him) said in al-Mughni (2/485): If he delays it (zakaat al-fitr) until after the day of Eid, he is sinning and he has to make it up. End quote. 

In al-Mawsoo’ah al-Fiqhiyyah (43/41) it says: The Maalikis, Shaafa’is and Hanbalis are of the view that the one who delays zakaat al-fitr until after the day of Eid when he is able to pay it is sinning and he has to make it up. End quote. 

The Standing Committee for Issuing Fatwas was asked: Is the time for paying zakaat al-fitr from after the Eid prayer until the end of that day? 

They replied: The time for paying zakaat al-fitr does not start after the Eid prayer, rather it starts at sunset on the last day of Ramadaan, which is the first night of the month of Shawwaal, and it ends with the Eid prayer, because the Prophet (peace and blessings of Allaah be upon him) enjoined that it should be paid before the prayer, and because of the report of Ibn ‘Abbaas (may Allaah be pleased with him) who said that the Prophet (peace and blessings of Allaah be upon him) said: “Whoever pays it before the (Eid) prayer, it is accepted zakaah, and whoever pays it after the prayer, it is (ordinary) charity.” It is permissible to pay it one or two days before that because of the report of Ibn ‘Umar (may Allaah be pleased with him) who said: The Messenger of Allaah (peace and blessings of Allaah be upon him) enjoined zakaat al-fitr at the end of Ramadaan … at the end of which he said: And they used to give it one or two days before that. But the one who delays it until after the proper time is sinning, and he has to repent from delaying it and give it to the poor. End quote. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked: I did not pay zakaat al-fitr because Eid came suddenly, and after Eid al-Fitr I kept asking about what I should do with regard to this matter. Is it waived for me or do I have to pay it? What is the reason behind it? 

He replied: Zakaat al-fitr is obligatory. Ibn ‘Umar (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) enjoined zakaat al-fitr. It is obligatory upon every Muslim, male and female, young and old, free and slave. If it so happens that Eid comes suddenly, before you can pay it, then you should pay it on the day of Eid, even if that is after the prayer, because if one misses the time of an obligatory act of worship for a reason, it must be made up when the reason ceases to apply, because the Prophet (peace and blessings of Allaah be upon him) said concerning prayer; “Whoever forgets a prayer or sleeps and misses it, let him pray it when he remembers it, for there is no expiation for it other than that.” And he recited the verse (interpretation of the meaning): “and perform As‑Salaah (Iqaamat‑as‑Salaah) for My remembrance” [Ta-ha 20:14]. End quote from Fataawa al-Shaykh Ibn ‘Uthaymeen (18/271). 

He also said: But if he delays it for a reason, such as forgetting or because there were no poor people to be found on the night before Eid,  then it will be accepted from him, whether he puts it back with his own wealth or leaves it until he finds a poor person comes.

The imam of the mosque should give this zakaah to the poor and needy. If there are no poor people in his city then he should send it to another city. 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) was asked about transferring zakaat al-fitr, and he replied: There is nothing wrong with transferring zakaat al-fitr to a city other than the city of the man who gave it, if that is done for a need because there are no poor people in his city. But if it is done unnecessarily, because there are people in his city who could accept it, then it is not permissible according to what some scholars have said. 

End quote from Fataawa al-Shaykh Ibn ‘Uthaymeen (18/318). 

And Allaah knows best.